Spherical Mirror Equation Calculator mechanism

Model scope

The equations themselves are correct for paraxial spherical mirrors, but the catalog specification needs an explicit sign convention, signed-input policy, infinity handling, and a defined image-characteristics classification before it can be marked PASS.

• The formulas are standard only under an explicitly stated sign convention; the specification does not define whether object distance, image distance, focal length, and radius are signed or positive magnitudes.
• The formula f=R/2 requires a signed radius or an explicit rule assigning the sign from mirror type; mirror type alone is insufficient as currently specified.
• The method for deriving the requested image characteristics (real or virtual, upright or inverted, magnified or diminished) is not specified.

Units and conventions

• R, f, do, and di must use the same length unit; magnification m is dimensionless.
• Test vectors use the real-is-positive convention: do>0 for a real object, f>0 and R>0 for a concave mirror, and f<0 and R<0 for a convex mirror.
• Under this convention, di>0 denotes a real image and di<0 a virtual image; m<0 denotes an inverted image and m>0 an upright image.
• The paraxial approximation applies to spherical mirrors and assumes small angles and rays near the optical axis.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "mirror_type": "concave",
    "R": "40 cm",
    "object_distance": "60 cm",
    "sign_convention": "real-is-positive"
  },
  "expected_outputs": {
    "f": "20 cm",
    "di": "30 cm",
    "m": -0.5,
    "image_characteristics": "real, inverted, diminished"
  },
  "working": "f=R/2=40/2=20 cm. 1/di=1/f−1/do=1/20−1/60=3/60−1/60=2/60=1/30 cm⁻¹, so di=30 cm. m=−di/do=−30/60=−1/2=−0.5. Since di>0, the image is real; since m<0, it is inverted; since |m|<1, it is diminished."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification admits zero-radius and do=f inputs that produce undefined results, and it leaves the sign convention for convex mirrors implicit. An implementation that performs plain arithmetic without validation or explicit sign-convention handling can return division-by-zero errors or physically incorrect image results.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json